22 papers · ranked by Valyu relevance
Sebastian Wallot, Dan Mønster
Using the method or time-delayed embedding, a signal can be embedded into higher-dimensional space in order to study its dynamics. This requires knowledge of two parameters: The delay parameter τ, and the embedding dimension parameter D. Two standard methods to estimate these parameters in one-dimensional time series…
Adam Śpiewak
for a diffeomorphism T of a compact manifold M and smooth observables h on M. Takens' embedding theorem shows that if k > 2 dim M, then ϕh,k is an embedding for typical h. We consider the probabilistic case, where for a given probability measure µ on M one allows selfintersections in the time-delayed embedding to occur…
Michael X Cohen
The number of simultaneously recorded electrodes in neuroscience is steadily increasing, providing new opportunities for understanding brain function, but also new challenges for appropriately dealing with the increase in dimensionality. Multivariate source-separation analysis methods have been particularly effective…
Xing-Yue Duan, Xiong Ying, Siyang Leng, Jürgen Kurths + 2 more
'Huanfei Ma'] Reservoir computing (RC), a particular form of recurrent neural network, is under explosive development due to its exceptional efficacy and high performance in reconstruction or/and prediction of complex physical systems. However, the mechanism triggering such effective applications of RC is still…
Zijian Wang, Peng Tao, Luonan Chen
Predicting time series is of great importance in various scientific and engineering fields. However, in the context of limited and noisy data, accurately predicting the dynamics of all variables in a high-dimensional system is a challenging task due to their nonlinearity and complex interactions. This study introduces…
Tom Lorimer, Rachel Goodridge, Antonia K. Bock, Vitul Agarwal + 3 more
Automated analysis of video can now generate extensive time series of pose and motion in freely-moving organisms. This requires new quantitative tools to characterize behavioural dynamics. For the model roundworm Caenorhabditis elegans, body pose can be accurately quantified from video as coordinates in a single…
Mitchell Ostrow, Adam Eisen, Ila Fiete
To generate coherent responses, language models infer unobserved meaning from their input text sequence. One potential explanation for this capability arises from theories of delay embeddings in dynamical systems, which prove that unobserved variables can be recovered from the history of only a handful of observed…
Daniel Wüstner, Henrik Helge Gundestrup, Katja Thaysen
Metabolic oscillations are a common phenomenon in cell biology. They are based on non-linear coupling of biochemical reactions and can show rich dynamic behavior including sustained and damped oscillations, as found, for example, in glycolysis of yeast and other eukaryotic cells. Metabolic oscillations are often…
Sebastian Wallot, Giuseppe Leonardi
This paper provides a practical, hands-on introduction to cross-recurrence quantification analysis (CRQA), diagonal cross-recurrence profiles (DCRP), and multidimensional recurrence quantification analysis (MdRQA) in R. These methods have enjoyed increasing popularity in the cognitive and social sciences since a…
Sarah A. M. Loos, Sabine H. L. Klapp
For stochastic systems with discrete time delay, the Fokker-Planck equation (FPE) of the one-time probability density function (PDF) does not provide a complete, self-contained probabilistic description. It explicitly involves the two-time PDF, and represents, in fact, only the first member of an infinite hierarchy. We…
Jonnel Jaurigue, Joshua Robertson, Antonio Hurtado, Lina Jaurigue + 1 more
'Kathy Lüdge'] Reservoir computing is a machine learning method that is well-suited for complex time series prediction tasks. Both delay embedding and the projection of input data into a higher-dimensional space play important roles in enabling accurate predictions. We establish simple post-processing methods that…
Richard E Rosch, Brittany Scheid, Kathryn A Davis, Brian Litt + 1 more
Many biological systems display circadian and slow multi-day rhythms, such as hormonal and cardiac cycles. In patients with epilepsy, these cycles also manifest as slow cyclical fluctuations in seizure propensity. However, such fluctuations in symptoms are consequences of the complex interactions between the underlying…
Michael Wibral, Nicolae Pampu, Viola Priesemann, Felix Siebenhühner + 5 more
'Hannes Seiwert' 'Michael Lindner' 'Joseph T. Lizier' 'Raul Vicente' 'Satoru Hayasaka'] In complex networks such as gene networks, traffic systems or brain circuits it is important to understand how long it takes for the different parts of the network to effectively influence one another. In the brain, for example…
Xiang Huang, Noah Cohen Kalafut, Sayali Anil Alatkar, Athan Z. Li + 3 more
Studying the temporal dynamics of neural activities is essential for understanding how neurons function. These dynamics often involve temporal delays between neurons that vary over time, revealing both their functions and how they interact within circuits. Recent techniques such as Neuropixels, depth electrodes, and…
Lina Jaurigue, Kathy Lüdge
Task specific hyperparameter tuning in reservoir computing is an open issue, and is of particular relevance for hardware implemented reservoirs. We investigate the influence of directly including externally controllable task specific timescales on the performance and hyperparameter sensitivity of reservoir computing…
Alberto Saucedo, Amirreza Yousefzadeh, Guangzhi Tang, Federico Corradi + 2 more
'Federico Corradi' 'B. Linares-Barranco' 'Manolis Sifalakis'] The role of axonal synaptic delays in the efficacy and performance of artificial neural networks has been largely unexplored. In step-based analog-valued neural network models (ANNs), the concept is almost absent. In their spiking neuroscience-inspired…
Dongyan Lin, Ann Zixiang Huang, Blake Aaron Richards
Neuroscientists have observed both cells in the brain that fire at specific points in time, known as “time cells”, and cells whose activity steadily increases or decreases over time, known as “ramping cells”. It is speculated that time and ramping cells support temporal computations in the brain and carry mnemonic…
Tony Lindeberg
This article presents an overview of a theory for performing temporal smoothing of temporal signals in such a way that: (i) temporally smoothed signals at coarser temporal scales are guaranteed to constitute simplifications of corresponding temporally smoothed signals at any finer temporal scale (including the original…
Authors not listed
Obtaining quantitative information about residence time behavior (i.e., the residence time distribution function) in realistic experimental systems is oftentimes experimentally challenging and numerically complex. The conventional way is to conduct very simple pulse or step tracer experiments or construct elaborate…
Dongyan Lin, Blake A. Richards
The representation of “what happened when” is central to encoding episodic and working memories. Recently discovered hippocampal time cells are theorized to provide the neural substrate for such representations by forming distinct sequences that both encode time elapsed and sensory content. However, little work has…
Christopher J. Cueva, Encarni Marcos, Alex Saez, Aldo Genovesio + 5 more
Our decisions often depend on multiple sensory experiences separated by time delays. The brain can remember these experiences and, simultaneously, estimate the timing between events. To understand the mechanisms underlying working memory and time encoding we analyze neural activity recorded during delays in four…
Authors not listed
Real-world datasets in chemical engineering and bioengineering processes--such as those from catalytic reactors, multiphase flows, polymerization reactors, bioreactors, and clinical trials--can often be unlabelled or disorganized, rendering the training of existing supervised learning models ineffective at learning the…